[jeromeflipo]

How small a fraction? Tesla is expected to produce between 80,000 and 90,000 Model S and X this year. With 80 Kwh battery pack on average (my guess), Tesla currently consumes 6.4 Gwh of Lithium-ion battery.

Back in 2013, the global production was estimated to be 35 Gwh (cf. Gigafactory announcement presentation).

How much has it grown in the past 3 years?

[Someone]

Eyeballing the chart in the article, and assuming kWh/car to have remained constant: by a factor of about 6.

The article also mentions 70% growth in the last year. Assuming equal growth in the other years, It would be about a factor of 5.