The Associated Press has spent months tracking a group of West Africans as they migrated illegally across Europe, confronting officialdom many times along the way but never effectively stopped, only delayed. The group's members have reached France and Germany just as they wanted.

Most, if not all, would never have made it if Europe's asylum controls were working.

How to fix Europe's broken asylum system is a key issue at an EU summit this week, and arguments are breaking down along painfully familiar lines.

Europe's central heavyweights want nations on the EU's frontiers such as Greece, Hungary, Italy and Spain to stop migrants at first base. But those front-line nations — struggling with some of the continent's highest unemployment rates and debt loads — argue that they can't bear the full burden, and that other EU members should agree to field a proportion of cases.

When the West Africans began their journey into the EU via Turkey in the east, they were able to cross not once but twice through EU border controls. In Greece and Hungary, police took names, photographs and fingerprints and issued temporary residency IDs that allowed the migrants to travel freely within the country. Both sides understood perfectly well that the IDs would allow the migrants — many of them traveling without passports or other bona fide IDs, and therefore free to give police whatever name and other personal details they wanted — to travel unhindered to the next border and leave.

To deter such behavior, a 1990 EU-wide agreement called the Dublin Convention dictated that asylum claims should be handled in the migrants' first point of entry. So if those migrants traveled deeper into the EU and filed for asylum in a second country, they would be deported back to the first.

But just as Greece's financial crisis has undermined the euro, it has helped to lay bare the practical limits of the Dublin Convention. Since 2008, an increasing number of EU countries have opted not to deport these migrants back to Greece, citing humanitarian concerns over the squalid and overcrowded conditions at its underfunded detention facilities.

Amnesty International underscored those concerns with a report Thursday declaring Greece's refugee holding facilities at a "breaking point," with a record 61,474 migrants already landing this year on Greek islands off Turkey's coast. Only two of the dozen-odd islands have formal refugee facilities.

The migrants also cannot be returned to Hungary. But in that case, it's primarily because of the anti-immigrant stance of its right-wing government, which makes no bones about its desire to ensure that most immigrants do not decamp there. Refugees told the AP that Hungarian police sometimes didn't even bother to take down correctly the names the migrants gave them, making it harder for other countries to connect the legal dots.

Hungary this week declared it would indefinitely suspend its observation of the Dublin Convention and would decline to take back migrants who had already gone west. That move followed Hungary's announcement it plans to build an immigrant-repelling fence on its border with non-EU member Serbia. Hungary also erected anti-immigrant billboards nationwide warning foreigners they "cannot take away Hungarians' jobs."

Such blockages in Greece, Hungary and many of the migrants' home nations mean that only a quarter of deportation orders in France, Germany and other migrant hot spots such as Britain and Sweden are enforceable, according to Minos Mouzourakis, asylum data coordinator for the Brussels-based European Council on Refugees and Exiles.

Once in their desired EU location, migrants can be stuck for years navigating a legal system that, in most cases, eventually gives them residency.

In France, for example, where more than 100,000 claimed for asylum last year, less than 20 percent of applicants win legal recognition as refugees in their first bid. This doesn't mean they're shipped anywhere else: The system requires two negative judgments, with time for appeals and opportunities to bolt to an EU neighbor and start over.

"Often it's really difficult (to deport), because for some countries, it's impossible to send them back," said Mylene Stambouli, a lawyer and activist for France's League for Human Rights, who provides legal advice to asylum applicants at refugee camps in Paris. "To Afghanistan, for example, there are no flights and no real diplomatic relations. So they stay here."

Associated Press reporters Maggy Donaldson in Paris and Pablo Gorondi in Budapest contributed to this report.