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Leading Brexiteer Owen Paterson wrote in an article in the Telegraph about fisheries:

At present, the UK provides 50 per cent of the EU’s waters but receives only a 25 per cent share of the Total Allowable Catch.

Is this assessment correct in both the facts and their implication? I.e. are the two parts separately true and are they also supposed to be connected that way, e.g. is the water area considered a principal factor in assigning fishing quotas in international law?

The whole point of that article seems to me is to claim that (when it comes to fisheries) the UK is getting taken advantage of (to borrow an expression common in foreign policy on the other side of the Atlantic nowadays)... and that this could all change after Brexit. It's hard not to read that as "we have 50% of the water, therefore we should also have 50% of the fish." Cue in mention of winning trade fishing wars, which is actually present in the title of the article: "After Iceland won the cod wars, their independent fisheries thrived. Britain can do the same".

From the European Environment Agency (an agency of the EU),

Combined EEZ of >15 million km2, the largest marine domain in the world

From the Commonwealth Parliamentary Association, the UK's exclusive economic zone (EEZ) is 6,805,586 sq km. Thus, the UK's waters are, at best, 45.4% of the EU's.

Regarding the Total Allowable Catch, The Conversation says

In 2015, the CFP allocated the United Kingdom a total of 612,612 tonnes of quota from more than 100 different fish and shellfish stocks. The total EU quota for these stocks was 2,069,202 tonnes, so the UK was allocated 30% of these fish (and shellfish) quotas.

As such, the UK was allocated 29.6% of the total allowable catch in 2015.

At present, the UK provides 50 per cent of the EU’s waters but receives only a 25 per cent share of the Total Allowable Catch.

The UK provides less than 50 percent of the EU's waters and received greater than 25 percent of the total allowable catch (in 2015). The claim is incorrect.

Note (per Fizz):

The total allowable catch is, according to Full Fact, set

based largely on how much [member states] fished in those areas in the 1970s, before the Common Fisheries Policy came into effect.

Thus, water area is not considered a principal factor in assigning fishing quotas. The fishing quotas are not assigned by "international law", but by the EU itself.

Interesting note:

From the Scottish Fishermen's Federation, between 2011 and 2015:

Non-UK European Union fishing boats landed about 700,000 tonnes of fish and shellfish, worth almost £530 million, from the UK EEZ each year on average.

UK fishing boats landed 92,000 tonnes of fish and shellfish, worth about £110 million, from other areas of the EU EEZ each year on average.

Note: The total allowable catch for 2019 can be calculated by adding all the numbers here, here, here, and here for 1) the UK and 2) all countries. I have not done this yet (it's a lot of numbers).