Radio emission from the high- and super-Eddington accreting active galactic nuclei (AGNs) has various origins: a persistent jet, the magnetized corona and the wind-like outflows. It is now still unclear which is the leading mechanism responsible for the observed radio emission and how the radio emission is related to other characteristic parameters such as the Eddington ratio and black hole mass. In this paper, we present the 5 GHz Very Large Array (VLA) observational results of a sample of 25 extremely high Eddington accreting supermassive black holes (EESBHs, the Eddington ratio close to or above one) from narrow-line Seyfert 1 galaxies, among which 22 sources are detected. Most of EESBHs show a compact radio structure from a few hundred parsecs to one-kiloparsec scale. We estimated the lowest star formation rate surface density required for producing the observed radio emission, and found it is higher than the largest value previously detected in circumnuclear starburst galaxies, implying that the radio emission is from the AGN activity. Along with a comparison sample, we find an overall inverse radio loudness and Eddington ratio correlation ranging from sub- to super-Eddington ratios. The high-Eddington and mildly super-Eddington AGNs (-0.5<log lambda_Edd<0.6) have a radio to X-ray luminosity ratio L_R/L_X~10^-5 to 10^-4 and a steep radio spectrum, supporting that the radio emission is from transient ejecta (outflows) of corona, however, the jet contribution cannot be fully ruled out. Our highly super-Eddington sources (log lambda_Edd>~0.6) have a flatter radio spectrum, along with its low radio luminosity: L_R/L_X~10^-5, their radio emission is likely dominated by a magnetized corona, and a radiation pressure caused jet is also proposed in this paper.
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