Mrk,421 was in its most active state around early 2010, which led to the highest TeV gamma-ray flux ever recorded from any active galactic nuclei (AGN). We aim to characterize the multiwavelength behavior during this exceptional year for Mrk,421, and evaluate whether it is consistent with the picture derived with data from other less exceptional years. We investigated the period from November 5, 2009, (MJD 55140) until July 3, 2010, (MJD 55380) with extensive coverage from very-high-energy (VHE; E$,&gt;,$100$,$GeV) gamma rays to radio with MAGIC, VERITAS Fermi -LAT RXTE Swift GASP-WEBT, VLBA, and a variety of additional optical and radio telescopes. We characterized the variability by deriving fractional variabilities as well as power spectral densities (PSDs). In addition, we investigated images of the jet taken with VLBA and the correlation behavior among different energy bands. Mrk 421 was in widely different states of activity throughout the campaign, ranging from a low-emission state to its highest VHE flux ever recorded. We find the strongest variability in X-rays and VHE gamma rays, and PSDs compatible with power-law functions with indices around 1.5. We observe strong correlations between X-rays and VHE gamma rays at zero time lag with varying characteristics depending on the exact energy band. We also report a marginally significant (∼ 3σ) positive correlation between high-energy (HE; E$,&gt;,$100$,MeV) gamma rays and the ultraviolet band. We detected marginally significant (∼ 3σ$) correlations between the HE and VHE gamma rays, and between HE gamma rays and the X-ray, that disappear when the large flare in February 2010 is excluded from the correlation study, hence indicating the exceptionality of this flaring event in comparison with the rest of the campaign. The 2010 violent activity of Mrk421 also yielded the first ejection of features in the VLBA images of the jet of Mrk,421. Yet the large uncertainties in the ejection times of these unprecedented radio features prevent us from firmly associating them to the specific flares recorded during the 2010 campaign. We also show that the collected multi-instrument data are consistent with a scenario where the emission is dominated by two regions, a compact and extended zone, which could be considered as a simplified implementation of an energy-stratified jet as suggested by recent IXPE observations.

Characterization of Markarian 421 during its most violent year: Multiwavelength variability and correlations